科研之友
微信
新浪微博
Facebook
分享链接
摘要
A deterministic weakening DW of the Belnap-Dunn four-valued logic BD is introduced to formalize the acceptance and rejection of a proposition at a state in a linearly ordered informational frame with persistent valuations. The logic DW is formalized as a sequent calculus. The completeness and decidability of DW with respect to relational semantics are shown in terms of normal forms. From an algebraic perspective, the class of all algebras for DW is described, and found to be a subvariety of Berman's variety K1,2. Every linearly ordered frame is logically equivalent to its dual algebra. It is proved that DW is the logic of a nine-element distributive lattice with a negation. Moreover, BD is embedded into DW by Glivenko's double-negation translation.
- 出版日期2019-4
- 单位中山大学
